Lebesgue (english) - meaning, definition, translation, pronunciation

Part of Speech

• Noun

Phonetic Transcription

• /lɛbˈɡeɪ/

Meaning and Usage

The term "Lebesgue" typically refers to Henri Léon Lebesgue, a French mathematician known for his contributions to measure theory and integration, particularly the Lebesgue integral. In various contexts, "Lebesgue" could also describe concepts or theorems associated with his work.

The frequency of use for "Lebesgue" is largely confined to mathematical and academic texts. It is predominantly used in written contexts, especially in higher education, research publications, and mathematical discussions.

Example Sentences

• The concept of the Lebesgue integral allows for the integration of a wider class of functions than the traditional Riemann integral.

• Концепция интеграла Лебега позволяет интегрировать более широкий класс функций, чем традиционный интеграл Римана.

• Understanding Lebesgue's contributions to measure theory is essential for advanced studies in analysis.

• Понимание вклада Лебега в теорию мер является важным для углубленного изучения анализа.

• The Lebesgue measure provides a way to assign a size or volume to sets in a more general context than classical measures.

• Мерам Лебега придаётся способ присвоить размер или объем множествам в более общем контексте, чем классические меры.

Idiomatic Expressions

While "Lebesgue" itself may not appear in many idiomatic expressions, it is essential in mathematical jargon. Below are examples of sentences using terms closely related to Lebesgue's work:

• Many mathematical proofs rely on Lebesgue’s criterion for convergence, highlighting the importance of rigorous analysis.

• Многие математические доказательства зависят от критерия сходимости Лебега, подчеркивая важность строгого анализа.

• To properly understand the intricacies of Lebesgue theory, one must first grasp basic measure concepts.

• Чтобы правильно понять сложности теории Лебега, сначала необходимо осознать основные понятия меры.

• The reliability of Lebesgue measure allows mathematicians to confidently approach more complex problems.

• Надежность меры Лебега позволяет математикам уверенно подходить к более сложным задачам.

Etymology

The term "Lebesgue" originates from the name of the mathematician Henri Léon Lebesgue, who introduced many fundamental concepts in measure theory in the early 20th century. The use of his name in mathematical contexts honors his pioneering work.

Synonyms and Antonyms

Synonyms: - Measure theory (referring to the broader field in which Lebesgue’s concepts are situated)

Antonyms: - Riemann (in the context of integration, as Riemann and Lebesgue integrals represent different approaches)

This breakdown provides a comprehensive understanding of the term "Lebesgue" in a mathematical context.